Method of forming three-dimensional images using multi-image hologram

ABSTRACT

A method of forming a three-dimensional image, comprising the general steps of taking a picture of an object illuminated by incoherent light through a lens array comprising a small number of lenses, projecting the image onto a diffusion screen through a lens array having the same performance as that of the lens array used for producing the image, and recording the projected image through the second lens array.

JJUJe SR United Stat Kimura et a1.

[111 3,765,741 [451 Oct. 16, 1973 METHOD OF FORMING THREE-DIMENSIONAL IMAGES USING MULTI-IMAGE HOLOGRAM [75] Inventors: Yoshiaki Kimura; Masanori Kawai,

both of l-lachiohji-shi, Tokyo; Tadashi Kasahara, Nakano-ku, Tokyo, all of Japan [73] Assignee: Konishlroku Photo Industry Co.,

Ltd., Tokyo, Japan 221 Filed: Dec. 27, 1971 211 Appl. No.: 212,535

[30] Foreign Application Priority Data Dec. 26, 1970 Japan 45/118907 [52] US. Cl. 350/35, 350/130 [51] Int. Cl. G02b 27/00 [58] ,Field of Search 350/35, 167, 130; 355/2 [56] References Cited UNITED STATES PATENTS 3,515,452 6/1970 Pole 350/35 3,608,993 9/1971 DeBitetto 350/3.5

OTHER PUBLICATIONS DeBitetto, Applied Optics, Vol. 8, No. 8, Aug. 1969, pp. 1740-1741.

Lohmann, IBM Technical Disclosure Bulletin, Vol. 10, No. 10, March 1968, pp. 1452-1454.

Primary Examiner-David Schonberg Assistant Examiner-Ronald J. Stern Attorney-Richard C. Sughrue et a].

[5 7] ABSTRACT A method of forming a three-dimensional image, comprising the general steps of taking a picture of an object illuminated by incoherent light through a lens array comprising a small number of lenses, projecting the image onto a diffusion screen through a lens array having the same performance as that of the lens array used for producing the image, and recording the projected image through the second lens array.

14 Claims, 24 Drawing Figures Patented Oct. 16, 1973 3,765,741

10 Sheets*Sh00t l Patented Oct. 16, 1973 10 Sheets-Sheet 2 FIG. 3

Patented Oct. 16, 1973 3,765,741

10 Shoe Ls-Sheat 5 Patented Oct. 16, 1973 3,765,741

10 Sheets-Sheet L Patented Oct. 16, 1973 3,765,741

10 Sheets-Sheet 5 FIG. I2

FIG. I3

Patented Oct. 16, 1973 10 Sheets-Sheet 6 o (cm) Patented Oct. 16, 1973 3,765,741

10 Sheets-Sheet 7 Patented Oct. 16, 1973 3,765,741

10 Sheets-Sheet 8 FIG. 20

Patented Oct. 16, 1973 10 Sheets-Sheet FIG. 2|

FIG. 22

Patented Oct. 16, 1973 3,765,741

10 Sheets-Sheet b:

FIG 23 IO8(IO8', IO8') METHOD OF FORMING THREE-DIMENSIONAL IMAGES USING MULTI-IMAGE HOLOGRAM BACKGROUND OF THE INVENTION This invention relates to a method of forming a threedimensional image by the use ofa multi-image hologram, and more particularly to a method of recording and reproducing a three-dimensional image of an object illuminated by incoherent light utilizing the art of holography employing a plurality of lenses.

It has been suggested that an image of an object illuminated by incoherent light should be reproduced in a three-dimensional way in copending Japanese Patent Applications Nos. 58954/70 and 80510/70 filed by an applicant equivalent to the assignee of this application. In the method suggested therein, a plurality of lenses having a high performance as that of the photographic lens are arranged in a matrix pattern to form a lens array and a plurality of images of the object illuminated with incoherent light viewed from a plurality of viewpoints corresponding to the respective apertures of the lenses are recorded on a photosensitive material in the first step thereof. In the second step, the photosensitive material is photographically processed into a positive through a reversal process and arranged at a position having the same relation with the lens array as is had at the time of recording, and the photosensitive material bearing the positive image is illuminated by coherent light to project the images onto the focal plane beyond the lens array where a photosensitive material for holography is located so that the images may be recorded on the photosensitive material for holography as an image hologram in cooperation with coherent reference light in incident to the photosensitive material.

7 In the third step, the hologram is illustrated by an incoherent light source having the expansion, i.e., the shape or the intensity distribution determined by the arrangement of a lens array, and the images viewed from the respective viewpoints are reconstructed without a dead space between the apertures in a space corresponding to the space occupied by the lens array in the recording.

As another method of eliminating the dead space, a method has been suggested in the foregoing Japanese Patent Application No. 80510/70 in which coherent and expanded light rays are used for the reference light in the second step and a point source or a source emitting somewhat expanded light rays is used for the reconstruction of the image in the third step. By the use of these methods, it is possible to reconstruct a threedimensional image of high sharpness presenting a right parallax variation accompanying the movement of the viewpoint.

In the foregoing two copending Japanese Patent Applications, a method is disclosed in which the range of vision within which the observer can see the threedimensional image is determined by the size of the lens array used in the first step. Accordingly, it is necessary to enlarge the lens array in the device used in the first step in order to obtain a range of vision of sufficiently large size. Two problems occur here in order to enlarge the device. One of the problems is the difficulty in designing and making the large size of multi-lens type camera in the sense of mechanical and optical engineering, and the other of the problems is the limit for the environment in which the large size of device can be handled and used. The former problem includes, for

example, the difficulty in providing a shutter mechanism which is operated for all the lenses constituting the lens array at the same time. This problem of the shutter is in fact very difficult and troublesome in a technical sense. The latter problem includes, for example, the difficulty in carrying the large device and in handling and using the device in the open air.

Another disadvantage inherent in the method disclosed in the foregoing copending applications is that the image obtained through the first step should be converted into a positive image in order that the image may be used in the second step. The photosensitive material used in the first step is required to be of large size and have comparatively high resolution. Such a positive photosensitive material, however, is difficult to obtain, since most of the commercially available types of the positive photosensitive material are of small size. Accordingly, on most occasions, negative type photosensitive material is used for recording the image in the first step. In the case where a negative photosensitive material is used in the first step, it is necessary to make a positive image by contact printing on another negative photosensitive material by the use of the negative image. Through this contact printing process, the resolution is reduced and further another problem occurs that the positioning of the positive image made by the contact printing relative to the lens array becomes diffcult.

In the foregoing two copending applications, Japanese Patent Applications Nos. 58954170 and 80510170, the space in which the image is reconstructed substantially corresponds to the original space where the ob ject existed. This is a disadvantage as well as an advantage. In other words, it is sometimes preferred to make the reconstructed image distorted to some extent intentionally to emphasize or reduce the three-dimensional effect. In the method disclosed in the foregoing patent applications, however, it is impossible to effect such an international operation to distort the image.

SUMMARY OF THE INVENTION The primary object of the present invention is to provide a method of forming a three-dimensional image using a hologram in which a sharp and reliable threedimensional image is formed.

Another object of the present invention is to provide a method of forming a three-dimensional image in which the abovementioned disadvantages are eliminated.

Other objects will be made explicit in the detailed description of the present invention hereinbelow described.

In order to accomplish the above described objects of the present invention, the method of forming a three-dimensional image in accordance with the invention comprises taking a picture of an object illuminated by incoherent light through a lens array consisting of a comparatively small number of lenses, projecting the image onto a diffusion screen through a lens array having the same performance as that of the lens array used for taking the image, and recording the projected image through a second lens array.

The present invention provides a method of forming a three-dimensional image basically composed of the following four steps:

First Step A plurality of lenses having as high performance as that of the photographic lens are arranged in one direction with equal intervals to form a lens array (first lens array) and a series of images (first image matrix) of different viewpoints of an object illuminated by incoherent light are obtained through said lens array.

Second Step The respective images of the first image matrix obtained in the first step are projected in turn onto a diffused screen through a lens array having the same performance as that of the lens array used in the first step. At the same time, the image projected on the diffused screen is recorded on a second photosensitive material through a second lens array consisting of a plurality of lenses having as high performance as that of the photographic lens arranged in the matrix patterns. In this recording step, a group of lenses in the second lens array extending in a direction perpendicular to the direction in which the first lens array extends correspond to one lens in the first lens array. Then, through a photographic process of the second photosensitive material exposed, the second image matrix is obtained.

Third Step The second image matrix obtained through the second step is illuminated by laser light from the back side and the images thereon are projected on a photosensitive material for holography through a lens array arranged in a matrix pattern having the same performance as that of the lens array (second lens array) used in the second step. The photosensitive material for holography is located at the position in the vicinity of the real image of the second image matrix, and the images projected thereon are recorded as an image hologram by means of the reference light which is coherent with the illumination light.

Fourth Step The image hologram obtained through the third step is illuminated by incoherent light source for reconstruction from the direction substantially opposite to the direction in which the reference light was produced in the third step. Thus, the real image of the lens array is reconstructed and the image of the object is observed from the position of the real image.

The dead space between the apertures can be eliminated by using a light source having expansion light for either the reference light in the third step or the illuminating light in the fourth step.

The advantages of the present invention are:

1. Being able to provide a method of forming a threedimensional image which can be made by the use of a black and white photosensitive material.

2. Being able to provide a method of forming a threedimensional image in which the duplication of the image can be carried out easily.

3. Being able to provide a method of forming a threedimensional image in which a three-dimensional image can be reproduced using a simple light source such as an ordinary incandescent lamp.

4. Being able to provide a method of forming a threedimensional image in which a three-dimensional image of a moving object can be formed.

5. Being able to provide a method of forming a threedimensional image in which the reconstructed image space can be optionally distorted.

6. And being able to provide a method of forming a three-dimensional image in which the magnification of the reproduction space can be optionally varied.

BRIEF DESCRIPTION OF THE DRAWINGS of the method in accordance with the first embodiment.

thereof;

FIG. 3 is a plan view showing a geometric explanation of the correspondence between the respective lens constituting the lens array having the same performance as that of the first lens array and the respective group of the lenses extending in a direction in the second lens array of the matrix pattern;

FIG. 4 is a perspective view showing the third step of the method in accordance with the first embodiment of the present invention;

FIG. 5 is a perspective view showing the fourth step of the method in accordance with the first embodiment thereof;

FIG. 6 is a perspective view showing an arrangement of the optical elements for carrying out a method I to properly orient the reconstructed image space in the first embodiment of the present invention;

FIG. 7 is a perspective view showing an arrangement of the optical elements in which the second step of the method in accordance with the first embodiment of the present invention is carried out without using a reflecting plane by utilizing the method I shown in FIG. 6;

FIG. 8 is a perspective view showing an arrangement of the optical elements for carrying out a method II to properly orient the reconstructed image space in the first embodiment of the present invention;

FIG. 9 is a perspective view showing an arrangement of the optical elements for carrying out a method IV to properly orient the reconstructed image space in the first embodiment of the present invention;

FIG. 10 is a perspective view showing an arrangement of the optical elements for carrying out a method V to properly orient the reconstructed image space in the first embodiment of the present invention;

FIG. 11 is a plan view showing the arrangement of the optical elements in the case where a difi'used screen of the reflection type is used as the diffused screen in the second step of the method in accordance with the first embodiment of the present invention;

FIG. 12 is a plan view showing the arrangement of the optical elements for the third step of the method in accordance with the first embodiment of the present invention in the case where the arrangement shown in FIG. 11 is employed in the second step in the first embodiment of the invention;

FIG. 13 is a plan view showing the arrangement in which a reflection type diffused screen is used in the second step of the method in accordance with the first embodiment of the present invention;

FIG. 14 is a geometric representation showing parameters having an influence on the reconstructed image space in the present invention and the construction of the reconstructed image space;

FIG. 15 is a graphic representation showing the relationship between a and a for various values of the parameter M when I,=I =l =l f =f and d,=Md

FIG. 16 is a geometric representation for explaining the discontinuity observed in the method of the present invention;

FIG. 17 is a geometric representation for explaining the amount of correction made in the case that a correction of distortion with moving the image plane is made;

FIG. 18 is a geometric representation for explaining the reconstructed image space when a correction of distortion with moving the image plane is made in the method of the present invention;

FIG. 19 is a perspective view showing the arrangement in which the first step of the method in accordance with the second embodiment of the present invention is carried out;

FIG. 20 is a plan view showing the arrangement in which the third step of the method in accordance with the second embodiment of the present invention is carried out;

FIG. 21 is a plan view showing the arrangement in which the fourth step of the method in accordance with the second embodiment of the invention is carried out;

FIG. 22 is a plan view showing the arrangement of the optical elements in which the first step of the method in accordance with the second embodiment of the present invention is carried out;

FIG. 23 is a perspective view showing the manner in which the second step of the method in accordance with the third embodiment of the present invention is carried out; and

FIG. 24 is a perspective view showing the manner in which the second step of the method in accordance with the fourth embodiment of the present invention is performed.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Now the present invention will be described in detail with reference to several particular embodiments thereof.

FIRST EMBODIMENT The first embodiment of the method in accordance with the present invention relates to a general method of forming a three-dimensional image and comprises the following four steps:

First Step A plurality of lenses having as high performance as that of the photographic lens are arranged laterally in a line at equal intervals to form a lens array (first lens array) and a series of images of different viewpoints of an object illuminated by incoherent light are recorded on a black and white photosensitive material by the use of the lens array. Through a phtotographic process of the photosensitive material bearing a latent image, a first image matrix is obtained.

Second Step The respective images of the first image matrix obtained in the first step are projected in turn onto a diffused screen through a lens array having the same perforrnance as that of the lens array used in the first step. At the same time, the image projected on the diffused screen is recorded on a second black and white photosensitive material through a lens array (second lens array) consisting of a plurality of lenses having as high performance as that of the photographic lens arranged in a matrix pattern at equal intervals. In this recording step, a group oflenses in the second lens array arranged in a direction perpendicular to the direction in which the lenses in the first lens array are arranged correspond to one lens in the first lens array. Thus, a large number of identical images are arranged in one direction on the second photosensitive material. By a photographic process of the second photosensitive material having a latent image, a second image matrix is obtained.

Third Step The second image matric obtained through the second step is illuminated by laser light from the back side and the images thereon are projected on a photosensitive material for holography through a lens array arranged in matrix pattern having the same performance as that of the lens array (second lens array) used in the second step, the photosensitive material for holography is located at the position in the vicinity of the real image of the second image matrix, and the images projected thereon are recorded as an image hologram by means of the reference light which is coherent with the illumination light.

Fourth Step The image hologram obtained through the third step is illuminated by incoherent light for reconstruction having expanded distribution from the direction substantially opposite to the direction in which the reference light was produced in the third step to reconstruct a real image of the lens array. Then, the image of the object is observed from the position where the real image is focused.

Now referring specifically to the drawing, each of the steps of the method in accordance with preferred embodiments of the present invention will be described in detail.

FIG. I shows the arrangement of the image forming system for the first step of the method of the present invention in accordance with the first embodiment thereof. The reference numeral 1 shows incoherent light illuminating an object 2 which is to be recorded and reproduced through the image forming method of the present invention. The reference numeral 3 shows a lens array consisting of a plurality of lenses having as high performance as that of the photographic lens arranged laterally in one direction (in the horizontal direction in the drawing) at equal intervals, which is referred to as a first lens array. The reference numeral 4 shows a black and white photosensitive material located at the position where the image of the object is focused on the back side of the lens array. This material is referred to as a first photosensitive material."

In the first step, a series of images of the object of different viewpoints are taken by the use of the arrangement. Although a shutter for controlling the exposure of the image recording is omitted in FIG. 1, it will be understood that a shutter mechanism may be provided which effects all the lenses in the array at a time or which effects the respective lenses one-by-one in turn in the case where a still object is taken. By a photographic process of the photosensitive material exposed to the light image, a series of images of different viewpoints, namely, a first image matrix, is obtained.

FIG. 2 shows an arrangement of the image forming system used for carrying out the second step of the method of the present invention in accordance with the first embodiment thereof. In FIG. 2 the reference numeral 5 shows a lens array having the same performance as that used in the first step, 6 shows the first image matrix obtained in the first step, 7 shows a diffused plate for making a diffused illumination, 8 shows incoherent light for illuminating the first image matrix 6, 9 shows a diffused screen, 10 shows a plane mirror, 9 shows a virtual image of the diffused screen 9 made by the plane mirror 10, 11 shows a lens array (second lens array) consisting of a plurality of lenses having as high performance as that of the photographic lens arranged in a matrix pattern at equal intervals, and 12 shows a second photosensitive material located behind the second lens array 11 at the focusing position of the diffused screen image. In the second step, the first image matrix 6 is located at a position behind the lens array 5 in the same relation to the lens array 5 as that made in the case of recording in the first step. The first image matrix 6 is illuminated by diffused incoherent light 8 through the diffused plate 7, and only one image in the first image matrix 6 is projected onto the diffused screen 9 through only one lens in the lens array 5 by opening only one shutter in front of the lens. Behind the diffused screen 9 is located a plane mirror 10 to form a virtual image 9' of the diffused screen 9, and the second lens array 11 and the second photosensitive ma terial 12 are located facing the virtual image 9 of the diffused screen. the second photosensitive material 12 is located at a position where the virtual image 9' is focused through the lens array 11 and a real image on the diffused screen is formed. The image projected and focused on the diffused screen 9 is recorded on the second photosensitive material 12 through the plane mirror 10 and the second lens array 11. In this recording step, an image of the first image matrix is recorded on the second photosensitive material 12 through only one group of lenses arranged vertically among the lens array 11 corresponding to the image projected (i.e., corresponding to the lens in the lens array 5 which projects the image). Consequently, the second pohtosensitive material 12 is provided with a plurality of identical images arranged vertically in a line.

Thereafter, another shutter belonging to another lens among the lens array 5 is opened to project a different image from the image matrix 6 onto the diffused screen 9. At the same time, the image projected onto the diffused screen 9 is recorded on the second photosensitive material 12 through another group of lenses arranged vertically among the second lens array 11. Such an operation is conducted for all the lenses in the first lens array 5 and all the images in the first image matrix 6. After all the images in the first image matrix 6 are recorded on the second photosensitive material 12 through the second lens array 11, the second photosensitive material 12 is photographically processed to obtain a second image matrix.

Now, the manner of making the correspondence between the respective lenses constituting the lens array 5 and the respective groups of vertically arranged lenses constituting the second lens array 11 of matrix pattern will be explained referring to FIG. 3. FIG. 3 is a plan view of the arrangement of the image forming system shown in FIG. 2, wherein the reference numeral 13 shows a first pohtosensitive material (first image matrix), 14 shows a first lens array (lens array having the same performance as that of the first lens array), 15 shows a diffused screen, 16 shows a plane mirror, 15 shows a virtual image of the diffused screen 15 made by the plane mirror l6, 17 shows a second lens array of matrix pattern, and the reference numeral 18 indicates a second photosensitive material. The first lens array 14 is assumed here to be a plurality of lenses arranged horizontally at equal intervals, where the number of the lenses is M and respective lenses are denoted as 14,, 14,, 14,,. Similarly, the second lens array 17 is assumed here to be a number of lenses arranged in a matrix pattern at equal intervals, where the number of lenses arranged horizontally is M and the number arranged vertically is N and the respective lenses of each horizontal group of lenses (consisting of N pieces of lenses) are denoted as 17,, 17,, 17

Assuming now an object point is denoted by A, the image of the object point A is recorded on the first photosensitive material 13 as a point a, through a lens 14, forming a part of the first lens array 14. Similarly, the point is recorded as a point a, through the lens 14, and as a point a through the lens 14,,. After the photographic process, the first photosensitive material 13 is located at the same position relative to the lens array having the same performance as that of the first lens array 14 as the position thereof relative to the first lens array 14 when the image was recorded thereon. First, the point image a, is projected onto the diffused screen 15 by use of the lens 14,. The point a, is projected onto the diffused screen 15 as a point a, and a virtual image of the point a, by the plane mirror 16 is formed at the position of 0,". Then, the point a," is recorded on the second photosensitive material 18 by use of a single one group of lenses 17, forming a part of the lens matrix of the second lens array 17. Then, the point a, is projected onto the diffused screen 15 through the lens 14, and the projected point a, is recorded on the second photosensitive material 18 by use of another group of the lenses 17,.

By repeating such operations for M times, all the images on the first photosensitive material 13 are transferred to the second photosensitive material 18. The images of the points a,", a,", a." formed through the lens groups 17,, 17,, 17,, are recorded on the second photosensitive material 18 as a,', a,"', a,,".

As will be understood, in general, the correspondence between the lenses in the first lens array 14 and the lenses in the second lens array 17 is made so that the lens 14, corresponds to the lens 17,, wherein the suffix j indicates the position of the lens numbered from the left when viewed from the back side of the lens array.

The third step of the first embodiment of the present invention is the step where one sheet of the image hologram is produced from the image matrix obtained through the second step by use of a coherent multirecording.

In FIG. 4, the arrangement of the image forming system used in the third step of the first embodiment of the present invention is shown. In FIG. 4, the reference numeral 19 indicates a second image matrix obtained through the photographic process of the second photosensitive material exposed in the second step, 20 shows a lens array of matrix pattern having the same performance as that of the second lens array used in the second step, 21 shows a diffused plate for giving a diffused illumination to the second image matrix 19, 22 shows laser light for illumination, 23 shows a photosensitive material for holography, and 24 shows laser light for reference light which is in coherent relationship with the laser light 22 for illumination. The reference numeral 25 indicates a point into which the laser light for reference light concentrates. As shown in FIG. 4, the second image matrix 19 is located behind the lens array 20 of matrix pattern' in the same relation therewith as the relation made in the second step when the image was recorded thereon. Further behind the second image matrix 19, a diffused plate 21 is located and illuminated by laser light 22 as shown in FIG. 4. The second image matrix 19 illuminated by laser light 22 is projected forward through the lens array 20. (Of course, although in projection, one lens in the lens array 20 corresponds to one image in the image matrix 19, if the screen is placed at the focusing position, different images of different viewpoints would be all superposed on the screen since all the images are projected at one time.) In the vicinity of the focusing position of the second image matrix projected through the lens array 20, a photosensitive material 23 for holography is placed. As laser light 24 concentrating into a point 25 is combined with the laser light projected from the lens array as a reference light, so that the images of the second image matrix 19 are holographically recorded on the photosensitive material 23 as an image hologram. Thus, obtained is an image hologram, after the photographic process of the photosensitive material, in which various images of different viewpoints are superposed in a coherent way.

The fourth step of the method in accordance with the first embodiment of the present invention is the step in which the reconstruction of the three-dimensional image is carried out by use of the image hologram obtained through the third step. FIG. 5 shows the arrangement of the image reconstructing system for carrying out the fourth step of the method of the present invention, wherein the reference numeral 26 shows the image hologram obtained through the third step, 27 shows an incoherent light source for reconstruction, 28 shows a color filter, 29 shows the real image of the lens array of matrix pattern used in the third step reconstructed from the image hologram 26, and 30 shows the positions of viewpoints. In this arrangement, by illuminating the image hologram 26 with expanded incoherent light source 27 having the diverging point at the position corresponding to the concentrating point (the numeral 25 in FIG. 4) of the reference light used at the time of recording the hologram, a real image of the lens array is reconstructed at a position corresponding to the position where the lens array was located in the third step. By locating eyes in the vicinity of the real image of the lens array 29, the images of the object viewed from the viewpoints corresponding to the position where the eyes are located can be seen. Accordingly, when viewed with both eyes, a three-dimensional image can be seen. Further, if the eyes are moved left and right, the image can be seen changing as the eyes move. In other words, by the present invention, one can see a three-dimensional image presenting parallax variation. The reference numeral 28 in FIG. 5 indicates a filter for selecting light of proper wavelength in order to reduce the color aberration in the real image of the lens array of matrix pattern.

Although an expanded light source is used in the fourth step as the illuminating light, namely, not a point source, a point source may be employed here if the reference light used in the third step should be an expanded light. The reason for employing the expanded light source is disclosed in the above-mentioned c0- pending applications, Japanese Patent Applications Nos. 58954/ and 80510/70.

In essence, by employing an expanded light source for either the reference light in the third step or the illuminating light in the fourth step, a dead space can be eliminated. Of course, the expanded light source may be employed for both the light sources. Although either alternative can be adapted to the present invention for the sake of simpification the following embodiments will be described with the expanded light only employed as the illuminating light for eliminating the dead space.

In the second step of the first embodiment of the present invention, a plane mirror 10 is employed between the transparent type difi'used screen 9 and the lens array 11 of matrix pattern as shown in FIG. 2. This is because the reconstructed image would be inverted when the first image matrix photographed in the first step of the first embodiment by using the first lens array is located at a position behind a lens array having the same properties as the first lens array in the same relation to the lens array as that made in the case of recording in the first step, and a transparent type diffused screen is employed into the system in the second step. However, it will be readily understood that the method of making finally a right image reconstructed is not limited to the employment of the plane mirror disposed between the transparent type diffusion screen and the lens array. Generally, it is only required to provide a single reflecting surface somewhere in some step of the method of the invention in order that the right image may be finally observed without inversion. Concretely, for example, there are the folloiwng five ways to prevent the inversion of the image in the present invention:

I. A plane reflecting surface is provided between the object and the first lens array in the first step so that the object may be recorded by way of the plane reflecting surface;

II. A plane reflecting surface is provided in the second step of the invention between the lens array having the same perfonnance as that of the first lens array and the transparent type diffused screen so that the first image matrix may be projected onto the diffused screen by way of the plane reflecting surface;

III. A plane reflecting surface is provided in the second step of the present invention between the transparent type diffused screen and the second lens array so that the image on the diffused screen may be recorded on the second photosensitive material by way of the plane reflecting surface;

IV. A plane reflecting surface is provided in the third step of the present invention between the second lens array and the photosensitive material for holography so that the second image matrix may be projected onto the photosensitive material for holography by way of the plane reflecting surface; and

V. A plane reflecting surface is provided in the fourth step of the method of the present invention between the image hologram and the viewpoint so that the reproduced image may be observed by way of the plane reflecting surface.

FIG. 6 shows the arrangement for carrying out the above method I, wherein the reference numeral 31 shows an object to be recorded and reconstructed, 32 shows a first lens array, 33 shows a first photosensitive material, 34 shows a plane mirror, and 31 shows a virtual image of the object 31 formed by means of the plane mirror 34. In the method I, the image of the object of different viewpoints is recorded on the first photosensitive material 33 by way of the plane reflecting surface.

In accordance with the method I, no reflecting surface is required in the subsequent steps and, accordingly, the plane mirror in the second step of the first embodiment of the method of the present invention as shown in FIG. 2 can be eliminated. The arrangement in which the second step of the first embodiment of the present invention is carried out without using the reflecting surface is shown in FIG. 7. In the drawing, the reference numeral 34' shows a lens array having the same performance as that of the lens array used in the first step, 35 shows the first image matrix obtained through the first step, 36 shows a diffused plate, 37 shows incoherent light for illuminating the first image matrix 35, 38 shows a diffused screen, 39 shows the second lens array and 40 shows the second photosensitive material. The correspondence between the lenses constituting the first lens array and the lens groups constituting the second lens array in the arrangement as shown in FIG. 7 should be so made that the j-th lens from the left of the first lens array when viewed from the back side corresponds to the j-th lens group from the right of the second lens array when viewed from the back side.

FIG. 8 shows the arrangement of the image forming system for carrying out the above method II. In the drawing, the reference numeral 41 shows a lens array having the same performance as that of the first lens array, 42 shows the first image matrix, 43 shows a diffused plate, 44 shows incoherent light for illuminating the first image matrix 42, 45 shows a plane mirror, 46 shows the diffused screen, 47 shows a second lens array, and 48 shows the second photosensitive material. The correspondence between the lenses constituting the first lens array and the lens groups constituting the second lens array in the arrangement as shown in FIG. 8 should be made in such a way that the j-th lens from the left of the first lens array when viewed from the back side corresponds to the j-th lens group from the left of the second array when viewed from the back side. The image on the first photosensitive material is recorded on the second photosensitive material according to the correspondence as described above.

The arrangement of the image forming system for carrying out the method III is shown in FIG. 2 as described hereinbefore.

FIG. 9 shows the arrangement of the image forming system for carrying out the above method IV, wherein the reference numeral 49 shows a second image matrix, 50 shows a lens array having the same performance as that of the second lens array, 51 shows a diffused plate, 52 shows laser light for illumination, 53 shows a plane mirror, 54 shows a photosensitive material for holography, 55 shows laser light for reference light and 56 shows the point of concentration of the laser light for reference light. In the case that such an arrangement is employed in the third step of the first embodiment of the present invention, a reflecting surface is not required in the other steps of the invention. Accordingly, in this case, the arrangement for the second step may be that shown in FIG. 7.

FIG. 10 shows an arrangement of the image recon structing system for carrying out the above method V, wherein the reference numeral 57 shows an image hologram, 58 shows an incoherent light source for reconstruction, 59 shows a color filter, 60 shows a plane mirror, 61 shows a real image of the second lens array reconstructed from the image hologram 57 and 62 shows the positions of the viewpoints for viewing the threedimensional image reconstructed.

So long as such an arrangement is employed in the fourth step for observation of the reconstructed image, no reflecting surface is required to be provided in any other ste antecedent thereto.

The five methods described above have been concerned with a method of obtaining the right orientation of the reconstructed image space or of obtaining the image space reconstructed without inversion under such a circumstance that the first image matrix is located relative to the lens array in the same relation therewith as that at the time of recording and further the image matrix is projected onto a transparent type diffused screen. (It should be understood that the right orientation referred to here should be considered to include such a state as that where the image that is not inversed is reconstructed with emphasized stereoscopic effector with distortion. The problem of the distortion of space will be described in detail hereinbelow.) If considering only one condition among the above two conditions where the transparent type diffused screen is used, it is possible to obtain the right orientation of the reconstructed image space without using a reflecting surface. This can be done by projecting the first image matrix obtained through the first step in the second step with the image inverted and arranged upside down.

The diffused screen used in the second step of the present invention for projecting the first image matrix thereon has been described to be of transparent type screen. This screen used on the second step of the present invention, however, may be a reflection type screen so long as it is of the diffused type. In the case where a reflection type diffused screen is used, the arrangement of'the image forming system for obtaining the second image matrix becomes slightly different from that shown in FIG. 2, FIG. 7 or FIG. 8, and is like that shown in FIGS. ll, 12 and 13.

FIG. 1 1 shows the arrangement of the image forming system used in the second step of the method of the present invention in which a reflection type diffused screen is used as the diffused screen. In FIG. 11 the reference numeral 63 shows the first image matrix obtained through the first step of the invention, and 64 shows a lens array having the same performance as that of the first lens array which consists of a plurality of lenses arranged in a direction perpendicular to the plane of the drawing sheet. The reference numeral 65 shows a diffused plate, 66 shows incoherent light for illuminating the first image matrix 63, 67 shows a half mirror, 68 shows a reflection type diffused screen, 69 shows a second lens array of matrix pattern, and 70 shows a second photosensitive material. In the drawing, the first image matrix 63 illuminated by diffused incoherent light 66 is projected on the reflection type diffused screen through the lens array 64 having the same performance as that of the first lens array. The image on the reflection type diffused screen 68 is recorded on the second photosensitive material 70 through the second lens array 69 by way of the half mirror 67. The correspondence between the lenses constituting the first lens array and the groups of the lenses constituting the second lens array is made in such a way that the j-th lens from the left of the first lens array when viewed from the back side corresponds to the j-th lens group from the left of the second lens array when viewed from the back side. If such an arrangement as described above is employed in the second step, it becomes necessary in the third step to project the second image matrix onto the photosensitive material for holography by way of a reflecting surface which is provided between the lens array having the same performance as that of the second lens array and the photosensitive material for holography as shown in FIG. 12. In the drawing, the reference numeral 71 shows a lens array having the same performance as that of the second lens array, 72 shows the second image matrix, 73 shows a diffused plate, 74 shows laser light for illumination, 75 shows a plane mirror, and 76 shows a photosensitive material for holography. (The reference light is omitted in the drawing.) It will be understood that if the reflecting surface is used in the third step, no reflecting surface is required in the subsequent fourth step.

Generally speaking, if such an arrangement as shown in FIG. 11 is used in the second step, the right orientation of the reconstructed image space can be obtained by using a reflecting surface in one of the steps among the first, third and fourth steps. A more simple arrangement for the second step in which a reflection type diffused screen is used as shown in FIG. 13. In the drawing, the reference numeral 77 shows a first image matrix, 78 shows a lens array having the same performance as that of the first lens array consisting of a plurality of lenses arranged in the direction perpendicular to the sheet of the drawing, 79 shows a diffused plate, 80 shows incoherent light for illuminating the first image matrix 77, 81 shows a reflection type diffused screen, 82 shows a second lens array of matrix pattern, and 83 shows a second photosensitive material. In the drawing, the first image matrix 77 illuminated by diffused incoherent light 80 is projected ontoa reflection type diffused screen through a lens array 78 having the same performance as that of the first lens array. The image on the diffused screen is recorded on the second photosensitive material 83 through the second lens array 82 disposed in front of the diffused screen. In this case also, the correspondence between the lenses constituting the first lens array and the groups of the lenses constituting the second lens array is made in such a way as that the j-th lens from the left of the first lens array when viewed from the back side corresponds to the j-th lens group from the left of the second lens array when viewed from the back side.

If such an arrangement as described above should be used on the second step, a reflecting surface is not required in any other steps of the method of the present invention.

As described hereinabove, different methods of effecting the right orientation of the reconstructed image space can be employed according to the various kinds of the diffused screen used in the second step and according to whether there is a reflecting surface or not. In any case, however, it is only required that the space which is finally obtained when the image is reconstructed is in the right orientation, which can be accomplished by any of the above five methods. The selection of the method should be conducted taking the situation of the whole system into consideration.

Any one of the above described methods can be applied to the other embodiments of the present invention as described hereinbelow. For the sake of simplification of explanation, however, the description will be limited in the following embodiments to the method in which a transparent type of diffused screen is used in the second step and a reflecting surface is disposed between the screen and the second lens array so that the image on the diffused screen is recorded on the second photosensitive material.

The space which is finally reconstructed has not been discussed so far. Now the influence on the reconstructed space finally obtained of the various parameters in the respective steps of the method of the present invention will be discussed hereinbelow.

The parameters which will influence the reconstruction image space, are as follows:

l. Focal length f of the lenses constituting the first lens array in the'first step.

2. Intervals d, between the lenses constituting the first lens array in the first step.

3. Distance 1 between the center of the object and the first lens array in the first step.

4. Depth a of the object (depth a, beyond the distance l 5. Distance 1 between the lens array having the same performance as that of the first lens array and the diffused screen in the second step.

6. Distance 1 between the diffused screen (or the virtual image thereof) and the second lens array in the second step.

7. Intervals d, between the lens groups constituting the second lens array in the second step.

8. Focal length f, of the lenses constituting the second lens array in the second step.

9. Distance 1 between the lens array having the same performance as that of the second lens array and the photosensitive material for holography in the third step.

Other than the parameters as described above, other factors such as the position of the reference light source in the third step or the position of the illuminating light source in the fourth step are considered to be the parameters influencing the reconstructed space. For the sake of simplification of explanation, however, the magnification of the holographic system in this case is assumed to be a unit.

Now, as shown in FIG. 14, it is assumed that an object point 0 located at a distance a, from a focusing plane (denoted by 2,) of the lenses (focal length f,, lens interval d,) constituting the first lens array apart therefrom by the distance I is taken by the use of the first lens array. When considering the i-th lens and H-1- th lens of the lens array, the point 0 is recorded on the first photosensitive surface 2, (apart from the lens array by the distance of l,) as two points of 0', and 0',.,,. The photosensitive material on which the image of the point is recorded is processed photographically and placed at the same position as that at the time of recording, and the image thereon is projected forward 15 through lenses L, and L, by the use of incoherent light.

If a diffused screen is at a position spaced apart from the lens array by the distance of I in front thereof (in the case where a diffused screen is at the focusing position), the images of the points and 0', are projected on the screen as the points 0, and 0, respectively. Then, it is assumed that a diffused screen is placed at a position spaced apart from the lens array in front thereof the distance of 1,. The plane on which the diffused screen is placed is referred to as plane E,. In order to project the image on the plane 2, onto the plane E',, it is necessary to control the focusing position of the lens to be at the position spaced apart from the lens array by the distance of 1,. In the case that the focal length of the lens is fixed, it is necessary to move the photosensitive material (image, namely, the first image matrix) from the plane 2, to the plane 2', in order to adjust the focusing position. If the image is moved to the position of the plane 2', and is illuminated from the back side, the points 0". and 0" (actually 0" and 0' are projected onto the diffused screen (on the plane Z,) as two pointsm and 6, Now the intersections of the optical axis of the lenses L, and L and the planes 2,, E 2,, Z, are denoted by n 7,, n",, n F n n",,,. In case where, as shown in FIG. 14, 0,0 y,,

(The minus sign represents the case where the object point is in front of the position of distance 1 from the lens array by the distance of a and if,

Assuming that the position of the object point projected is spaced from the position of the distance I, from the lens array by the distance of 0,,

Similarly, the distance y, between the two points projected on the photosensitive material for holography in the third step is represented by the formula:

where f, is the focal length of the second lens array, 1, is the distance between the diffused screen and the second lens array in the second step, d, is the interval between the lens group of the second lens array, and I. is the distance between the lens array having the same performance as that of the second lens array and the photosensitive material for holography in the third step.

The depth of the object point reconstructed in the fourth step (assuming the reconstruction is formed at a position spaced apart from the position of the distance I. by the distance of a.) is represented by 4 K): 0/: I m] From the formulae (1) to (5),

(8) from the formula (7) is obtained, which means that a is linear with respect to a and the reconstruction is not distorted. (Example II) I I: I; 1.

fr f:

d, Md,

from the formula (7) is Etained, which means that the reconstructed space can be distorted by various parameters. (In the formula (1 l), the minus sign shows the case where the object point is in front of the position of distance I, from the lens array by the distance of (1,.)

FIG. 15 is a graphical representation showing the value of the a in relation with a, when M 2 and M 56. (The graph shows the case where the object point is behind the position of distance I, from the lens array.) From the graph, it is apparent that the space is contracted when M l and expanded (feeling of threedimensional effect emphasized) when M l.

In the fourth step, the object point 0 is reconstructed on the photosensitive material for holography located at the position spaced apart from the viewpoint by the distance of I, as a number of points which can be seen with both eyes as a three-dimensional object point. In

this case, the separation of the adjacent two points on the photosensitive material for holography causes a feeling of discontinuity as the eyes move. This can be explained with FIG. 16. When the viewpoint is moved from L, to L' the image of the object point reconstructed on the hologram surface 2H jumps from to 0' abruptly, which causes a feeling of discontinuity in the observer's eyes. In order to prevent this phenomenon, it is necessary to make the angle between LQO, and L',0', smaller than the angular resolving power of eyes.

This discontinuity feeling can be eliminated if l l /1, Aa

In view of the formula (6), where Am is the angular resolving power of eyes. Accordingly, it is necessary to select the parameters so as to satisfy the condition of the formula (12). In practice, the object point projected is not reconstructed as a perfect point, but as a somewhat expanded point due to aberrations of the lens system and diffraction of the light at the apertures of the lenses. The conditions for eliminating the discontinuity feeling can be regarded as somewhat looser than the formula (12).

Generally, the object to be reconstructed into the three-dimensional image is not a point as discussed hereinabove, but a body having some expansion or size. Therefore, even if the discontinuity feeling due to that jump" is eliminated, at one point, there occurs this jump at other points. Of course, it is desired to reduce said jump as far as possible in the vicinity of the point noticed in the object in case where an object having some size is reconstructed.

Now considging the case where the object point is on the plane g, (focusing plane corresponding to the plane including the point noticed of the object, see FIG. 14), in the first step of the method of the present invention, the formula (6) becomes with a 0 which generally does not become zero. This means that there occurs said jump in the reconstructed image even if the object point is on the plane I, Therefore, it is required to reduce as much as possible the jump" of the image in the reconstructor space with respect to the point noticed to obtain a three-dimensional image with little feeling of discontinuity. This is accomplished by the concept of a correction of distortion with moving the image plane which will be described hereinbelow.

Now referring to FIG. 17, noticing the central lens L, and the k-th lens L, in the lens array, we consider the case that the object point 0 at the intersection point of the optic axis of the lens L, and a plane 2, at the distance of I from the lens L, is photographed by the use of the first lens array (focal length f interval between lenses (1,).

The image of the point 0 is recorded on th e first photosensitive material at the position (plane (1) spaced apart from the lens array by the distance of l, as two points 0', and 0, by the lenses L, and L,,. Then, in order to make the focusing position of the lens array be on the plane 2 spaced apart from the lens by the distance of 1,, the first photosensitive material photographically processed, i.e., the first image matrix, is moved parallel to the position (plane T spaced apart from the lens array by the distance of I',. By illuminating the image matrix from the back side with diffused light, the images of the points 0",, (same as the point 0,,) and 0:, (same as the point 0',) are projected on the plane 4', as the points 0" and 0' by the lenses L, and L, respectively. The length 0'0" is represented by, in view of the formula (2) which generally does not become zero (when l 1,).

If the point 0",, is then moved to the point 0",,, the image of the point 0", on the plane P, which is shown at 0 is superposed on the point 0", so that y, 0. (where 0" is an intersection of the optical axis of the lens L, and the plane and 0 is an intersection of the plane F, and the extension of a line including L, and 0 The length of movement Ax is represented by By substituting l 1,, f for I, and 1' This result shows that it is possible to bring a plane having no jump" of image into alignment with the plane 1,", by moving laterally (in the direction in which the lenses of the lens array are arranged) the image corresponding to the k-th lens by the length Ax represented by the formula 15) or (16). The length Ax is linear with respect to k, and the images correspoding to the respective lenses of the lens array are recorded on a sheet of photosensitive material. Accordingly, in practical operation, the first image matrix is moved for the first lens from the central lens by the length Ax, represented by A371: 1 (H's/ s] "Uh/ 11) lfl 1 2)/( l 1 1) 1)] and is moved for the second lens by the same further length Ax The lateral movement by the length is repeated in turn for the rest of the lenses.

Although the result obtained through the formula object point in general, in the case where a correction of distortion with moving the image plane has been effected, will be discussed.

Assuming now that, as shown in FIG. 18, the focusing position of the lenses (focal length f interval between 

1. A method of forming three-dimensional images comprising the steps of:
 1. obtaining at least one first image matrix comprising a series of images of different viewpoints of an object illuminated by incoherent light by use of a first lens array comprising a plurality of lenses arranged in one direction at equal intervals and a first photosensitive material positioned to receive said images;
 2. projecting each image of said first image matrix on a diffuser screen one by one in turn through a second lens array having the same performance characteristics as those of said first lens array;
 3. obtaining at least one second image matrix on a second photosensitive material by recording the images of said first image matrix as each image of said first image matrix is projected on said diffuser screen, this step being accomplished by use of a third lens array comprising a plurality of lenses arranged in a two-dimensional matrix pattern, there being correspondence between said first and second image matrices in such a way that one image of said first image matrix corresponds to one group of said second image matrix, said group being arranged in a direction perpendicular to the direction in which the images of said first image matrix are arranged;
 4. illuminating said second image matrix from the back side thereof with at least one first source of coherent light, and focusing said second image matrix with a fourth lens array having the same performance characteristics as those of said third lens array onto a third photosensitive material for forming a holographic object beam, while simultaneously
 5. illuminating said third photosensitive material with one or more reference beams of light coherent with the light from said first source of coherent light so as to form a hologram, said one or more reference beams eminating from one or more second sources of coherent light, each of which second sources of coherent light is related to a source of incoherent light used in the next step of this process such that at least one of each related pair is an expanded light source, thereby recording an image hologram of said second image matrix on said photosensitive material in multiple superposition; and
 6. forming a real image of said object by illuminating said image hologram with one or more incoherent light sources, which incoherent light sources are related to said one or more second sources of coherent light as previously recited, from the directions opposite to those of said one or more reference beams use in the preceding step, whereby a three-dimensional image free from dead spaces may be viewed from the vicinity of the real image of said first lens array.
 2. projecting each image of said first image matrix on a diffuser screen one by one in turn through a second lens array having the same performance characteristics as those of said first lens array;
 2. The method of forming three-dimensional images as defined in claim 1 wherein said diffuser screen is of the transparent type and a plane mirror is used in one of said steps, thereby obtaining a right orientation in the reproduction space.
 3. The method of forming three-dimensional images as defined in claim 1 wherein said diffuser screen is of the reflection type.
 3. obtaining at least one second image matrix on a second photosensitive material by recording the images of said first image matrix as each image of said first image matrix is projected on said diffuser screen, this step being accomplished by use of a third lens array comprising a plurality of lenses arranged in a two-dimensional matrix pattern, there being correspondence between said first and second image matrices in such a way that one image of said first image matrix corresponds to one group of said second image matrix, said group being arranged in a direction perpendicular to the direction in which the images of said first image matrix are arranged;
 4. illuminating said second image matrix from the back side thereof with at least one first source of coherent light, and focusing said second image matrix with a fourth lens array having the same performance characteristics as those of said third lens array onto a third photosensitive material for forming a holographic object beam, while simultaneously
 4. The method of forming three-dimensional images claimed in claim 1 wherein a plurality of first color-separated image matrices are obtained in the first step of the process recited in claim 10 using black and whilte photosensitive materials and a plurality of color filters, a plurality of second color-separated image matrices are obtained in the third step of said process, each of said plurality of second color-separated image matrices corrresponding to one of said plurality of first color-separated image matrices, a plurality of reference beams are used in the fifth step of said process, each of said plurality of reference beams being directed on said photosensitive surface for holography from a different direction and each of said plurality of reference beams being used with only one of said plurality of second color-separated image matrices, and a pluRality of incoherent light sources are used in the sixth step of said process, each of said plurality of incoherent light sources being color-filtered in a manner corresponding to the color separation of the corresponding one of said first color-separated image matrices, whereby a color three-dimensional image is formed.
 5. The method of forming three-dimensional images claimed in claim 4 wherein said plurality of reference beams are of different wave lengths corresponding to the wave lengths recorded by the corresponding one of said plurality of first color-separated image matrices.
 5. illuminating said third photosensitive material with one or more reference beams of light coherent with the light from said first source of coherent light so as to form a hologram, said one or more reference beams eminating from one or more second sources of coherent light, each of which second sources of coherent light is related to a source of incoherent light used in the next step of this process such that at least one of each related pair is an expanded light source, thereby recording an image hologram of said second image matrix on said photosensitive material in multiple superposition; and
 6. forming a real image of said object by illuminating said image hologram with one or more incoherent light sources, which incoherent light sources are related to said one or more second sources of coherent light as previously recited, from the directions opposite to those of said one or more reference beams use in the preceding step, whereby a three-dimensional image free from dead spaces may be viewed from the vicinity of the real image of said first lens array.
 6. The method of forming three-dimensional images claimed in claim 1 wherein a plurality of first color-separated image matrices are obtained in the first step of the process recited in claims 10 using black and white photosensitive materials and a plurality of color filters, a single second image matrix is recorded on color photosensitive material in the third step of said process, a plurality of first sources of coherent light are used in the fourth step of said process, each of said plurality of first sources of coherent light being of a different wave length corrresponding to one of the colors of the color separation made in the first step of said process, a plurality of reference beams are used in the fifth step of said process, each of said plurality of reference beams being directed on said photosensitive material for holography from a different direction, and a plurality of incoherent light sources are used in the sixth step of said process, each of said plurality of incoherent light sources being color-filtered in a manner corresponding to the wave length of the corresponding one of said plurality of reference beams, whereby a color three-dimensional image is formed.
 7. The method of forming three-dimensional images claimed in claim 6 wherein each of said plurality of reference beams is of a different wave length corresponding to the wavelength of the one of said plurality of first sources of coherent light with which it is used.
 8. The method of forming three-dimensional, images claimed in claim 6 wherein said single second image matrix is simultaneously illuminated by more than one of said plurality of first sources of coherent light.
 9. The method of forming three-dimensional images claimed in claim 1 wherein a single first image matrix is obtained in the first step of the process recited in claim 10 using color photosensitive material, a plurality of second color-separated image matrices are obtained in the third step of said process using black and white photosensitive materials and a plurality of color filters, a plurality of reference beams are used in the fifth step of said process, each of said plurality of reference beams being directed on said photosensitive surface for holography from a different direction and each of said plurality of reference beams being used with only one of said plurality of second color-separated image matrices, and a plurality of incoherent light sources are used in the sixth step of said process, each of said plurality of incoherent light sources being color-filtered in a manner corresponding to the wave length of the corresponding one of said plurality of reference beams, whereby a colored three-dimensional image is formed.
 10. The method of forming three-dimensional images claimed in claim 9 wherein a plurality of first sources of coherent light are used in the fourth step of said process, each of said plurality of first souces of coherent light being of a different wave length corresponding to one of the colors of the color separation made in the third step of said process.
 11. The method of forming three-dimensional images claimed in claim 9 wherein said plurality of reference beams are of different wave lengths corresponding to one of the colors of the color separation made in the third step of said process.
 12. The method of forming three-dimensional images claiMed in claim 1 wherein a single first image matrix is obtained in the first step of the process recited in claim 10 using color photosensitive material, a single second image matrix is recorded on color photosensitive material in the third step of said process, a plurality of first sources of coherent light are used in the fourth step of said process, each of said plurality of first sources of coherent light being of a different wave length, a plurality of incoherent light sources are used in the sixth step of said process, each of said plurality of incoherent light sources being color-filtered in a manner corresponding to the wave length of one of said plurality of first sources of coherent light, whereby a colored three-dimensional image is formed.
 13. The method of forming three-dimensional images claimed in claim 12 wherein said plurality of reference beams are of different wave lengths corresponding to the wave lengths of the one of said plurality of first sources of coherent light with which it is used.
 14. The method of forming three-dimensional images claimed in claim 12 wherein said single second image matrix is simultaneously illuminated by more than one of said plurality of first sources of coherent light. 